If you have a Boltzmann distribution, you still know all the microstates—you just have a probability distribution over them. Time evolution in contact with a zero-entropy object moves probability from one microstate to another in a predictable way, with neither compression nor spreading of the probability distribution.
Sure, this requires obscene amounts of processing power to keep track of, but not particularly more than it took to play Maxwell’s demon with a known cup of tea.
If you have a Boltzmann distribution, you still know all the microstates—you just have a probability distribution over them. Time evolution in contact with a zero-entropy object moves probability from one microstate to another in a predictable way, with neither compression nor spreading of the probability distribution.
Sure, this requires obscene amounts of processing power to keep track of, but not particularly more than it took to play Maxwell’s demon with a known cup of tea.